I solved my problems. I installed the "custom" bootloader for each Rom and the "black screen" problem is now gone.
I have the following problem.
When I install one of the latest rom e.g.
4.1.2 AOKP for the Galaxy Tab 10.1
Android 4.1.1 - CyanogenMod 10 Preview
then I have this problem:
When I turn off with the "Power"-Hardbutton, then it...